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Hot electron harvesting via photoelectric ejection and photothermal heat relaxation in hotspots-enriched plasmonic/photonic disordered nano-composites Long Wen, Yifu Chen, Li Liang, and Qin Chen ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01156 • Publication Date (Web): 16 Nov 2017 Downloaded from http://pubs.acs.org on November 17, 2017
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Hot electron harvesting via photoelectric ejection and photothermal heat relaxation in hotspots-enriched plasmonic/photonic disordered nano-composites 1#
2,3#
Long Wen, Yifu Chen,
3
Li Liang, and Qin Chen
1,3,*
1
Institute of Nanophotonics, Jinan University, Guangzhou 511443, China
2
School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China
3
Key Lab of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of
Sciences (CAS), Suzhou 215123, China *
#
Corresponding author:
[email protected], equal contribution
ABSTRACT: The ability of plasmonic nanostructures to harvest photons beyond the traditional band-to-band photovoltaic conversion of semiconductors has stimulated intensive research activities in hot electron. As an emerging strategy for energy-harvesting, photodetection and photocatalysis, realization of broadband and efficient plasmonic absorption with easily constructed metal-semconductor (M-S) nanosystems is essential for improving its photoelectric efficiency, whilst minimizing the cost and complexity of fabrication. Here, we report an approach for near-infrared (NIR) photodetection by combining the randomly and densely packed photonic nanostructures with ultrathin plasmonic coatings. Relying on the Au covered disordered silicon nanoholes (SiNHs) M-S platform, the efficient plasmonic absorption, strong field localization and together with random nature facilitate the broadband photon-energy conversion from both photoelectric hot electron ejection and photothermal hot electron relaxation. Spectral- and time resolved studies reveal that the proposed Au-SiNHs device is capable of tracking fast-varying NIR signals via hot electron emission process, with a photoresponsivity around 1.5-13 mA/W at wavelengths ranging from 1100 to 1500 nm. With a detailed theoretical analysis based on phenomenological model, different loss mechanisms involving in the hot electron related photoelectric process were described quantitatively and a large improvement potential was identified in the proposed hot electron harvesting platform. In addition, we demonstrated that the closely distributed random voids and tips in the Au-SiNHs structures enable the formation of substantial amount of hot-spots which can significantly elevate the local temperature through the relaxation of the non-ejected hot electrons, and therefore generate the obvious photothemal mediated photoresponse under voltage driven conditions. Keywords: hot electron, photodetection, photothermal, plasmonic, quantum efficiency
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The photovoltaic (PV) effect driven by valence-to-conduction band transition of carriers sets the physical foundation for the current mainstream of energy-harvesting or photodetection devices. Over the past decades, the upgrading of the PV materials has propelled the development of different types of semiconductor-based photodetectors with operating wavelengths extending from ultraviolet to 1
mid-infrared regime. However, the applicable semiconductor materials are limited by their band gaps. For example, silicon cannot be used for photodetection based on band-to-band transition for the photons with energy below 1.1eV. Aiming at the development of silicon-compatible optoelectronic devices which facilitate on-chip optics-electronics integrations, Germanium (Ge) and III-V semiconductors epitaxially grown or wafer bonding on Si with extended spectral photoresponse have therefore been attracting extensive interests for telecom communication and other infrared applications.2,3 On the contrast, there are several alternative mechanisms enabling sub-band gap photoresponse in semiconductors, e.g. two-photon absorption, bulk defect-mediated absorption and surface defect-mediated absorption have been proposed previously for silicon devices.4,5 Without extra process complexity or cost for introducing foreign absorbing materials on silicon, the implementation of these sub-band photon-to-electricity conversion strategies in practice, however, has been hampered by problems in efficiency, speed, reliability issues and so on. Energy dissipation and transfer associated with the nonradiative decay of electromagnetic waves in metallic nanostrcutures has received great attentions in the field of plasmonic for exploring its 6
7
applications like thermo-optics modulation, plasmonic photothermal therapy and solar water distillation.8 Beyond above plasmonic heating events, important breakthroughs enabling photon-to-electricity conversion were achieved very recently via ejection of hot electrons at the plasmonic metals-semiconductor (MS) or –insulator-metals (MIM) interfaces.
9-20
The spectral
response of such a photoelectric effect depends on the barrier height that energetic electrons should overcome rather than on the band-to-band transition of a semiconductor.11,17 Extended photoresponse on Si platform is thereby attainable by means of integrated plasmonic elements, as has already been demonstrated very recently.
9,12,14-16,20
There are two critical issues that determine the
conversion efficiency of hot electron devices, i.e. the optical absorption and the internal quantum efficiency (IQE). Thanks to the superiority in the near-field light concentration and resonant tunability, 12
various plasmonic trapping schemes like the extraordinary optical absorption, elongated plasmonic micro-trench antenna15,18 and MIM resonator10,20 have been successfully employed for the purpose of
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enhancing the metallic absorption and therefore hot electron generation from the optical perspective. Unfortunately, carrier transport and ejection in metals are relatively un-efficient processes compared to semiconductor materials, manifesting in previously reported ultra-low IQE especially for NIR wavelengths (less than 1%).9,12 As a consequence, the photon-to-electricity efficiency of hot electron devices relies more heavily on their electrical design. Since the mean free path of hot electron in 21,22
metal in only several to several tens nanometers,
it has been reported that the plasmonic
resonance with high field localization (i.e. hot spots) adjacent to the barrier of MS or MIM can 12
significantly increase the collection possibility of hot electrons. Furthermore, it is possible to gain IQE enhancement with shortened transporting path of energetic carriers by straightforwardly thinning down the thickness of plasmonic absorber layer.23,24 Concerning the importance of hot electron extraction, a framework for systematically analyzing the impacts of hot spots control and plasmonic absorber thickness is needed. It has been known for long in photovoltaic studies that randomly textured photonic structures (e.g. nanowire, nanohole and pyramid) allow perfect impedance matching to the incident radiation and efficient light trapping ability over a broad spectral range by light diffusion, multiple-scattering, and 25-27
light coupling among the neighboring scatterers.
Combining the disordered photonic architectures
with plasmonic elements offers an alternative strategy to improve plasmonic absorption through the interplay between photonic/plasmonic scattering and large amount of plasmonic hot spots excited by localized resonance.
8,20,28,29
Compared to elaborate periodic counterparts, disordered nanostructures
require relatively simple and low-cost fabrication process, and their optical properties are expected to be less sensitive to the incident angle and polarization state. In this paper, we report on the design and realization of efficient hot electron harvesting in NIR region on Si platform using ultrathin plasmonic metal coated random Si nanohole (SiNH) structures. The densely and randomly packed Au/SiNH junctions at a deep nanoscale lead to emergence of subwavelength areas supporting enhanced electric field, resulting in broad-band and efficient metal absorption. Relying on this hot spot-enriched platform, we present a detailed comparison of the spatial distributions of hot spots as well as thickness changes of plasmonic coating layer on the hot electron conversion. DESIGN PRINCIPLE OF HOT SOPTS-ENRICHED AU/SI DEVICE The hot electron device we proposed herein consists of a structured Si substrate with closely
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packed random SiNHs and an ultrathin conformal gold film coating, as shown schematically in Figure 1a. The thin plasmonic absorber also serves as an anode as it forms Schottky contact with n-type Si. Regarding on the importance of spatial distribution of the hot electrons generated in plasmonic absorber, two illumination modes, i.e. the front-side and back-side illumination (incidence entrances the device from the structured side and non-structured Si side, respectively) were studied and compared. Ohmic fine wire electrode (200 nm thick aluminum) with low filling ratio was prepared and thermally treated on the other side of Si substrate before the growth of double layers of dielectric film which we used to achieve optical impedance with air. For the back-side illumination mode, the 150nm Silicon nitride and 100nm Silicon oxide function as dual AR coatings that minimize the specular reflection loss less than 5% for the wavelengths of 1150-1900 nm (see SI, Figure S1).
Figure 1. (a) Schematic of the proposed plasmonic hot electron photodetector. (b-c) Field and Pabs distributions of the device operating at the front and back-illumination modes. A typical morphology of Au/SiNHs from our experiments is adopted in these simulations.
The short mean free path length of hot electron transport in gold raises a critical requirement to optimize the spatial distribution of the plasmonic absorption for the sake of hot electron collection. 30
Three-dimensional simulations using finite element method (Comsol multiphysics ) were performed to examine the field localization effect of the two illumination modes. As shown in Figure 1b, for the back-side illumination mode, the NIR light transmitted through Si strikes on the nano-structured Au/Si interfaces and forms strongly localized field distributions in these areas. On the contrary, for the front-side illumination mode plasmonic absorption tends to occur at the Au/air interfaces. The volumetric power absorption Pabs shown in Figure 1c was calculated from the divergence of the Poynting vector, and described as:
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P = ω|E| ε
(1)
where ω is angular frequency, ε′′ is the imaginary part of the material permittivity and E is the electric field distribution. Considering the energy loss from the resistive contribution (Pr)31 herein, the hot electron generation can be written as32: G = (1 − P )P /ℏω, where ℏ is the reduced Planck constant. As illustrated in Figure 1c, the energy of incident radiation in the back-side illumination mode can be absorbed in metal with the spatial locations more adjacent to the M-S junctions than the front-side illumination mode. The observed difference in the spatially localized plasmonic absorption and thus the G of these two illumination modes therefore is expected to result in a great deviation in their electrical performance. Referring to the blue arrows schematically shown in Figure 1b, for the front-illumination case hot electrons generated at the Au-air interface should transport through the metal and therefore undergo significant recombination issues like electron–electron scattering. However, when the device operates at the back-illumination mode, hot electrons generated adjacent to the junctions can be ejected directly into silicon and then swept away by the built in field of M-S junction. Consequently, the back-illumination mode gains much higher IQE than the other mode, thus is more favorable for photodetection from an electrical aspect. Further, in Figure 1b the back-illumination case yields abundant photonic modes as verified by the complex field pattern in the Si. These photonic modes will contribute to the metal loss directly or be coupled with plasmonic effect allowing the Au/SiNHs to sustain a large local density of states. Thus, from the optical aspect, the back-illuminated structure can absorb more efficiently compared to the front illuminated structure.
DEVICE FABRICATION AND OPTIMIZATION OF THE SPATIAL DISTRIBUTION OF HOT SPOTS Figure 2a shows the process flow of the proposed random Au/SiNH device. First, an ultrathin (5 nm) Au film was sputtered on the Si substrate (1-10 Ω cm, n-type, double polished) and then subjected into the rapid thermal process (RTP) chamber. After the thermal dewetting process with a fixed duration of 1 min under the protection of nitrogen, the continuous Au film changes to different nano-structured morphologies depending on the applied dewetting temperature.33 Since the formation of nano-viods or defects appears at random locations and times on the flat surface, there is an inherent randomness in the dewetted nanostructures for both their spatial order and morphology. The nano-structured Au layer was used as the metal catalyst film for the metal assisted chemical
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etching34 (MACE, HF:H2O2:alcohol=15:2:60). During MACE, silicon was etched only directly underneath the Au catalyst film, resulting in a disordered SiNH morphology with a mean depth around 100 nm. The Au catalyst film was then completely removed by gold etching solution (I2/KI). Next, a thin layer of Au was deposited by sputtering and forms conformal plasmonic coating on the random SiNHs. Finally, ohmic fine wire contact and dual AR layers were prepared on the non-structured Si side. The calculated electric filed distribution (λ=1500 nm) and absorption spectra for the three structures are summarized in Figure 2c-d.
Figure 2.(a) Fabrication procedure for the proposed Au/SiNH photodetectors. (b) Scanning electron microscopy (SEM) images of the Au/SiNHs fabricated using Au templates dewetted at different temperatures. (c) The calculated field distributions of the Au/SiNHs. From left to right, the plots correspond to the regions marked by the dashed green boxes of three samples shown in (b), where the field data was extracted from the plane sliced at half height of the SiNHs. (d) Calculated absorption spectra of the three Au/SiNH structures in (c). The insets show the side-views of the back-illuminated numerical model for the Au/SiNHs, and the SEM image of the SiNHs after the MACE process.
The above nanofabrication steps have distinctive advantages for producing of nanogap-rich and disordered plasmonic/photonic composite over a large area. The average size and separation of metal/SiNH nanoislands can be finely tuned by imposing different dewetting temperature for the etching template fabrication procedure. The dewetting process of Au is initiated from the break-up of
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the thin film and at low dewetting temperature of 400 °C the Au domains become tortuous or worm-like. With increasing the temperature, the Au atoms prefer to aggregate into larger and more round-shaped nano-island morphology and the surface coverage of Au domains decreases. The resulting Au/SiNHs fabricated with the thermally dewetted Au etch templates imposing different temperatures (400, 500, 700 °C) are shown in Figure 2b. Since MACE reactions occur only at the footprints of the Au catalysts, the Au/SiNHs have exactly the same shapes and spatial distributions with the thermally dewetted Au templates. The disordered plasmonic/photonic composites are expected to give rise to more favorable light coupling and excitations of high density of localized plasmon modes in a broad spectral region. Nevertheless, there are differences in shapes, distributions and feature sizes among above three Au/SiNH structures, leading to considerable variation in optical property. To quantitatively evaluate their light trapping ability, numerically reconstructed structures using the realistic lateral morphology of the Au/SiNHs (calculation domains are 1×1 μm2 in size, marked by the green boxes in Figure 2b) were studied via the three-dimensional FEM simulation. The mimicked SiNHs have a depth of 100 nm and a 20 nm thick Au was assumed to be conformally coated on the SiNHs. In these simulations, the back-side illumination mode was adopted, as illustrated in the inset of Figure 2d. For the worm-like Au/SiNHs (left, Figure 2c) which contain the smallest and most close-packed features are characterized by the coexistence of spatially localized and delocalized modes over the entire structure. The presence of large number of hot spots at random nano-void and tips of this structure leads to the pronounced and broad-band plasmonic absorption enhancement, as verified by its absorption spectra shown in Figure 2d. On the contrary, the Au/SiNHs (right, Figure 2c, 700 °C dewetted case) with larger and more round-shaped features exhibit field distributions that only the localized modes are pronounced and mainly concentrated at the sidewalls of the isolated clusters. These localized modes as a result of collective plasmonic resonances have large field amplitudes but interact weakly from each other, leading to relatively poor light absorption especially for long wavelengths, as illustrated in Figure 2d. From the above studies, we can clearly identify that the Au/SiNHs structures fabricated with the low temperature dewetting procedure have optimum lateral morphologies that sustaining hot spots extend over mesoscopic dimensions, therefore is more favorable for plasmonic light trapping and thus was adopted in the design of the hot electron devices in the subsequent experiments.
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SPECTRAL RESPONSIVITY OF THE HOT ELECTRON CONVERSION Besides the optimization of the lateral morphology of SiNHs, we fabricated the hot electron devices that have different thicknesses of the plasmonic coatings and compared their performances regarding both the optical absorption and photo-electrical response. Figure 3a shows the measured absorption spectra of the Au/SiNHs and planar reference (Au on non-structured Si) devices, operating at the back illumination mode. The planar device has poor light absorption which attributes to the fact of that the continuous flat Au film is reflective to the whole NIR wavelength regime. Significantly higher light absorption can be observed in the nano-structured devices. With the decreasing thickness of plasmonic coating, the light absorption of Au/SiNH devices increases gradually at long wavelengths. For the thinner plasmonic coatings, electromagnetic waves (EM) can penetrate through the metal and interact with the Au/air interface. The multiple scattering and inter-coupling of the localized modes excited at the Au/SiNH and Au/air interfaces together enhance the light absorption in the thin plasmonic coatings. However, for the thick Au layer, the interaction of EM field between the two interfaces is blocked and the incident radiations are only moderately trapped at the Au/SiNH interfaces. Combining the benefits from the use of thin metal layers and the back illumination mode, the Au/SiNH junction allows the hot electrons to be collected more efficiently. The Au/SiNH structures we used for hot electron devices have a worm-like morphologies and the nano-clusters are inter-connected (as shown in Figure 2b), rendering the ultrathin metal coatings with 20 nm thick to be electrically continuous. As illustrated in Figure 3b, the ultrathin Au coated SiNH device exhibits a clear rectifying behavior in its I-V characteristics, due to the formation of Schottky contact between Au and n type Si. Fitting the measured I-V curve in the forward bias voltage region with the Richardson-Schottky equation can provide essential information that identifies the quality of the Schottky junction.35 As shown in the inset of Figure 3b, the fitted curve is in a good agreement with the measured result. The derived Schottky parameters, i.e. the ideality factor (n) and the barrier height (ФB) are 4.5 and 0.66 eV, respectively. The larger-than-unity ideality factor as well as the relatively low ФB (compared to planar Au-Si contact) is often observed experimentally in nanoscale diodes which can be ascribed to the inhomogeneities at the M-S interfaces. As we outlined previously, the hot electron harvesting is driven by the thermal emission of hot electrons at the M-S junctions and both the efficiency and the cut-off property depend strongly on the barrier height. Consequently, the barrier height we deduced herein serves as a useful electrical parameter for the further
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opto-electrical characterization of the hot electron devices.
Figure 3. (a) Measured absorption spectra of the Au/SiNH devices with different thicknesses of Au coatings. The result of a planar reference device with 20 nm thick Au deposited on non-structured sample is also included. Note that, the back illumination mode was used for all of these measurements, i.e. the Si side with AR coatings is the illuminating surface. (b) The measured current-voltage (I-V) plot of the typical Au/SiNH device with 20 nm thick Au conformal coating. The inset shows the fitting results for the forward bias regime of device. (c) Measured responsivities of the proposed and reference devices (dotted lines). The solid lines represent the theoretical predictions using Fowler model. Different CF values were adopted to achieve the best fitting with the experimental spectra. The inset shows the IQE spectra for the 20 nm Au case, calculated from the Fowler responsivity. (d) Time-dependent responses of the optimized devices operating at two illumination modes.
The wavelength-dependent photoresponse measurements were performed via a home-made external quantum efficiency (EQE) characterization system. The hot electron devices were operated at the back illumination mode, with a Xenon lamp that was spectrally filtered by a grating monochromator. The incident light was pre-calibrated by a commercial InGaAs photodiode (cut-off at 1900 nm) and its spectrum-dependent power is provided in the SI (Figure S2). The photocurrent signal in response to the chopped illumination (333Hz) was measured through the lock-in amplifier technique. Figure 3c shows the measured responsivity of the Au/SiNHs devices with varying Au coating thickness. The result of the planar reference device (20 nm Au on Si) is also given in this plot. The responsivity of planar reference is quite low at the wavelengths shorter than 1200nm and can be safely attributed to the Si response. In contrast, the responsivities of all the Au/SiNH devices exhibit a
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large enhancement (approximately 19-fold, as indicted in the plot) over the planar reference device at this wavelength regime. This fact reveals that incorporating of Au/SiNH in the device can also greatly amplify the Si absorption via the near-field localization and multiple scattering. All of the measured responsivity curves of the Au/SiNH devices feature with another distinct metallic response that extends to far beyond the Si cut-off wavelength. As illustrated by the green area, this metallic response gradually decreases with the increasing wavelength of the incident light. Meanwhile, there is clear evidence that the Au/SiNH device with 20 nm thick plasmonic coating layer outperforms the thicker cases, with current responsivity in range of 10 to 1.4 mA/W in the wavelength region from 1200 nm to 1550 nm. The observed metallic response stemming from the photoelectric mechanism of hot electron can be qualitatively interpreted by the Fowler emission theory. By taking the optical absorption into account, the modified Fowler equation gives an expression for the external quantum efficiency:
ƞ!(λ) = C# A(λ)(hν − Ф' ) /hν
36
(2)
where CF is the Fowler emission coefficient, A(λ) is the experimental absorption spectra of the Au/SiNH devices, ФB is the Schottky barrier height and hν is the energy of incident photon. The ƞe(λ) can be related to the spectral current responsivity as follow:
R(λ) = ƞ! (λ)q/hν
(3)
where q is the elementary charge. We assume that all the three Au/SiNH devices have an identical barrier height of 0.73 eV, slightly larger than the value we deduced from the dark I-V curves. Importantly, CF was adopted as a device-specific parameter that gives an account of the electrical performance, since it is in direct proportion to the IQE which can be described as: ƞ! (λ)/A(λ). As demonstrated in Figure 3c, the Fowler formula using CF as the sole fitting parameter provides a very good approximation to all the measured current responsivities of Au/SiNH devices at the metallic response region. It is also convenient for us to discern the contribution of hot electron emission versus the Si photovoltaic response. For instance, at a wavelength of 1100 nm, the responsivity of the hot electron mechanism is found to be 13 mA/W. In principle, the Fowler formula indicts a clear cut-off point, at which the incident light with photon energy equal to the barrier height cannot overcome the energy barrier of the M-S junction. Thus, the predicted cut-off wavelength of the Au/SiNH devices is estimated to be 1700 nm. Unfortunately, in our measurements, the incident power is only few μW for the wavelength of 1550 nm, and decreases further into the sub-μW scale at the wavelengths
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approaching 1700nm. Together with the low and continuously decreased responsivity of Au/SiNH devices at these wavelengths, it is quite difficult to obtain satisfying signal-to-noise ratio in these measurements. A very interesting point to note is that the fitted CF which represents the IQE of the devices under investigation appears to be dependent on the thickness of Au coating layers, as confirmed in the Figure 3c. The Au/SiNH device containing the thinnest plasmonic coating layer (i.e. the 20 nm case) has a CF value of 0.12, higher than the other two cases. This finding provides clear evidence that thinning down the thickness of plasmonic absorber can efficiently improve the probability of hot electron ejection, regarding on the finite mean free path of the electrons in metals.
21,22
As illustrated
in the inset of Figure 3c, we observed an IQE approaching 1.7% at the band edge of Silicon, which is much higher than the values reported by previous antennas or grating-Schottky photodetector in the wavelength region where silicon does not absorb.
9,12
Apart from the dependency of IQE on the
thickness, the impact of the spatial distribution of the plasmonic absorption is also critical. This is already apparent when comparing the responsivity of the planar reference with the Au/SiNH devices. As shown in Figure 3a, the planar device has a metallic absorption around 10% at wavelengths beyond the Si absorption cutoff, which is one-ninth of the absorption of the Au/SiNH device with same metal thickness. However, the corresponding response of planar device is negligible, at least hundred times smaller than the Au/SiNH device. In the previous studies, we had demonstrated that the Au/SiNHs operating at the back illumination mode have more favorable field localizations for the hot electron collection. To verify this point, we then measured the responsivity of the ultrathin Au/SiNH device operating at two different illumination modes and the results are summarized in Figure 3d. To ensure high signal-to-noise ratio, the measurements were accomplished by using the high-power supercontinuum laser coupled with the tunable NIR filter (both from NKT Photonics). Photocurrent signal was directly recorded by a sourcemeter. As expected, the back illumination mode exhibits much higher responsivity against the front illumination mode. The absorption spectra of the front illumination mode can be found in the SI (Figure S3). The enhancement of responsivity of the back illumination mode cannot be solely attributed to its higher absorption. For example, at the wavelength of 1400nm, the back illumination mode has 6-fold enhancement on responsivity over the front illumination mode, but the absorption is only 4-fold. Consequently, it elucidates that the back illumination mode also yields a substantial improvement in its electrical aspects. In accordance with
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our previous statements, the back-illumnation mode with localized absorption adjacent to the M-S junction has higher IQE and therefore the more efficient hot electron photodetection.
THEORETICAL DESCRIPTION OF THE DEMONSTRATED QUANTUM EFFICIENCY In order to better understand and assess above experimentally demonstrated performances of the proposed devices, phenomenological IQE models accounting for the contributions of the resistive loss as well as the internal relation of hot electron were developed. There are three competing energy transfer mechanisms in NIR regime that contributes to the plasmon decay of Au 31
nanostructures, i.e. the resistive, geometry and photon-assisted transitions. Only the geometry and photon-assisted transitions lead to the hot carrier generation, whereas the resistive one dissipates thermally. Depending on the feature size and shape of nanostructures, the resistive loss contribution (Pr) varies in the range of 10~40% at NIR wavelengths for Gold.
31
The hot electron energy distribution is critical for the collection because only the hot electrons with sufficiently high energy and momentum are able to traverse the M-S barrier. The hot carrier energy distribution upon photon excitation can be determined by combining the electron density of 37
states (EDOS) of metal with the Fermi distribution function:
∝ D(E − E. )f(E − E. )D(E)(1 − f(E))
(4)
f(E) = 1/(1 + e(12 )/34 )
(5)
where D(E) is the EDOS of real Au materials, f(E) is Fermi distribution function, and Ef is Fermi level 38
of Au (~5.53 eV ). Figure 4a shows the calculated hot electron distribution as a function of incident wavelength and the energy (relative to Fermi level, i.e. E=Eh-Ef) of excited hot electron. Considering a barrier height of 0.73 eV for the M-S contact, the hot electrons with energy smaller than ФB have no chance of being emitted but contribute to the thermalization losses, resulting in energy dissipation around 68% and 90% at the wavelength of 1100nm and 1500nm, respectively.
Apart from above loss mechanisms, the internal relaxation of hot electrons including of
momentum mismatch at the interface and transport losses due to electron-electron scattering should be considered further for theoretically assessing of the IQE. Due to the complexity of the proposed Au/SiNH structures, accounting above momentum and transport attenuation processes with fully three-dimensional numerical solutions is a considerable work that goes beyond the scope of this paper. To this end, we follow Christine’s phenomenological models
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24
and simplify the M-S
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configuration by assuming a thin Au film (20nm, corresponding to our experiments) on a semiconductor forming a single Schottky barrier.
Figure 4. (a) The calculated hot electron distribution as a function of incident wavelength and the energy of photoexcited hot electrons relative to the Fermi level of gold. (b) Schematic drawing depicts the phenomenological models of hot electron harvesting. (c) Theoretical IQE calculated from the phenomenological models with ФB of 0.73 eV. The experimentally fitted IQE is re-plotted in here for the sake of comparison. (d) Prediction of IQE of the proposed device with decreasing M-S barrier height, calculated from the t=8 nm thin-film phenomenological model.
As schematically shown in Figure 4b, this IQE model is based on assessing the emission probability of hot electrons as a function of their energy, taking into account resistive loss, multiple reflections within the metal film and energy transport loss. The theoretical IQE of Au/Si junction is therefore given by: :;
:;
IQE = 8Ф (1 − P )D(E)P(E)dE / 8= D(E)dE
